Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C7 |
No aliases for this group.
| Fitting | C22×C4×C72 ⋊ C2 |
| Sylow | C72 ⋊ #123 |
390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
Polycyclic presentation:
2^5,7^2|c^2=e,b^a=be,c^a=cd,f^a=f^6,g^a=g^6398 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 735);